NEW YORK — In a flashback to 2013, the Standard & Poor's 500-stock index rallied to an all-time closing high Thursday, bringing the bullish vibe back to Wall Street.

After flirting with a new closing peak the previous three sessions, the benchmark U.S. stock index finally blasted through the milestone, jumping 0.5% to close at 1854.29 and topping mid-January's previous record close of 1848.38.

The all-time high, its second of the new year after 45 record closes in 2013, officially marks the end to its recent 5.8% "pullback." The Russell 2000 index of small cap stocks also closed at a record high, as did the broad Wilshire 5000.

Though the Dow Jones industrial average remains 2% below its all-time closing high, Wall Street no longer seems petrified that turbulence in emerging markets, which rattled markets earlier this month, will lead to financial contagion.

Investors also seem to have dissuaded themselves from the notion that less stimulus from the Federal Reserve, bad winter weather and political unrest in the Ukraine are enough to derail the expected uptick in U.S. economic growth this year.

The new high comes as the bull market nears its fifth birthday on March 9. It also continues a long stretch without a full-fledged correction, or a drop of 10% or more. The S&P 500, which soared 30% last year, suffered its last correction in 2011.

"To have only a 6% correction is a great sign of strength," says Donald Luskin, chief investment officer at TrendMacro. "It is telling us that U.S. stocks might have been tired but didn't want to go down. They just took a little nap."

But Jim Stack, editor of InvesTech Research, says investors shouldn't rush into the market in a speculative way. The reason: The bull is nearing its fifth birthday, which is already more than a year longer than the average bull market.

"If you look at where we are on the Wall Street road map, we are in the latter innings of the bull," says Stack. "And while bear market warning flags, (such as signs of a recession and the start of Fed rate hikes) are absent so far, investors should not follow the same aggressive strategy as they did early in the bull market."

What's powering the latest record-setting run:

• Confidence in the economy. Sure, economic data have been coming in weak early in 2014. But Wall Street is convinced the bulk of the weakness is due to the weather, and that growth will pick up when the temperatures rise.

"The economy is not sprinting, but it's finally back on its feet," Luskin says.

• New Fed chief reassures Wall Street. Fed Chair Janet Yellen has reaffirmed that the central bank will remain market-friendly, just as it was under previous chief Ben Bernanke. Her testimony today before the Senate Banking Committee was again reassuring to investors, says Rod Smyth, chief investment officer at RiverFront Investment Group.

"Yellen reaffirmed that the 'doves,' (or policymakers that see the need for more stimulus to heal the job market and economy) are in charge," says Smyth.

• The slide in long-term interest rates. The yield on the 10-year Treasury note started the year at 3.03%, and most investors thought it would spike even higher. But, due to the weak economic data recently, the yield has actually dropped to 2.64%.

"Falling rates have been a key support to the stock market," says Jeremy Siegel, a finance professor at the Wharton School at the University of Pennsylvania.

The fact that the emerging markets turbulence didn't morph into a crisis circa 1997-1998 has also been a bullish driver, Siegel adds.

"That's been another big key," say Siegel, adding that he thinks fair value for the S&P 500 is closer to 2000, or roughly 8% higher.

A key test for the stock market will come this spring, Siegel adds. That's when Wall Street will find out if the economic soft patch was truly weather-related or not. If the weakness is due to more than just snow and ice, the market could run into some trouble.